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Helmholtz resonator

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Helmholtz resonator is a type of an acoustic resonator, which consists of a cavity (or enclosed volume) of air which is connected to the environment through a small opening. The enclosed air resonates at a single frequency that depends on the volume of the cavity and the geometry of its opening.

Physical background

When excited by a force, a mass suspended on a string (spring-mass system) performs harmonic oscillations with a dedicated frequency:

f_o = \frac{1}{2\pi}\sqrt{\frac{k}{m}}

fo: Fundamental frequency
k: Spring stiffness
m: Mass

  • The higher the stiffness, the higher the frequency.
  • The higher the mass, the lower the frequency.

In acoustics, a volume forms a spring (like an air pump) with
V \propto k^{-1}
and air in a duct/bottle neck acts as a moving mass with
L \propto m
. This results in a very similar calculation of the fundamental frequency:

f_o = \frac{c}{2\pi}\sqrt{\frac{A}{V \cdot L}}

fo: Fundamental frequency
c: Speed of sound
A: Opening area
L: Length of the opening
V: Volume of the cavity

  • The smaller the volume the higher the frequency
  • The longer the neck the lower the frequency

Calculate the resonant frequency f0[Borchia]:



Examples developed in the frame of the ACTOR project[ACTOR]:
The ACTOR project
Name: Online guide to room acoustics for musicians

Participants: Malte Kob (Detmold University of Music) [PI], Martha de Francisco (McGill University), Fabien Lévy (Hochschule für Musik und Theater Leipzig), Kit Soden (McGill University), and Caroline Traube (Université de Montréal)

Aim: Creation of an internet-based guide for musicians that describes in layman terms the fundamentals of acoustic features of musical instruments, 
stages, performance and rehearsal rooms using visual and 
auditory examples from, e.g., the ODESSA project.

1. A flickering candle flame in front of a double bass f-hole: The candle flickers due to the interaction between the resonant frequencies of the f-hole and the air vibrations produced by the instrument's sound waves.

2. Blowing a bottle: When you take a bottle, and blow over the open neck, you hear a sound: that's the resonant frequency of the bottle. If you fill the bottle (or empty it) with a liquid, you will hear the frequency shift: the fuller the bottle (smaller volume), the higher the frequency.

3. An open car window: The booming sound you hear when opening a car window is a result of the interaction between the airflow around the car and the cabin's resonant frequency.


  • Helmholtz resonators can be used to amplify or attenuate specific frequencies of sound waves. For example, they can be incorporated into the design of wind instruments like clarinets, oboes, and organ pipes to improve the richness and quality of specific notes.
  • Helmholtz resonators can be used as resonance absorbers in noise control and room acoustics to absorb narrowband, low-frequency room modes. For example, in concert halls, theaters, studios, schools, offices, and conference rooms.
  • Helmholtz resonators can be used in loudspeaker construction in the form of bass reflex enclosures.


  • [REF]
  • [unsw] Helmholtz Resonance (
  • [Borchia] Borchia, D. "Helmholtz Resonator Calculator". Available at: Accessed: 21 August 2023.
  • Thomas Görne: Tontechnik. 1. Auflage, Carl Hanser Verlag, Leipzig 2006, ISBN 3-446-40198-9.
  • Hermann von Helmholtz: Die Lehre von den Tonempfindungen. 6. Auflage, S. 73, S. 600–603, 1913
  • ACTOR project:
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